Sensitivity study of the hardening soil model parametersbased on idealized excavation

B. Gebreselassie, H.-G. Kempfertlnstitute of Geotechnics and Geohydraulics, UniversihJ of Kassel, Germany

Keywords: excavation, constitutive soil model, drained, undrained, finite element method

ABSTRACT: The paper presents a study of the sensitivity of the hardening soil model (HSM)parameters to a change of values in an idealised excavation in normally consolidated soft clay soil.The HSM is a constitutive elasto-plastic-cap model which is presently impiemented in the PLAXISfinite element program. By varying one parameier and keeping the other parameters constant, theinfluence of each parameter on the performance of the excavation can be studied. ln this way, iican be proven whether the model parameters did pedorm exactly as they may theoretically beexpected to pedorrn

1 lntroduciion

The influence of the hardening soil model parameters under drained conditions on the stress-strainand volume change behaviour has been discussed in the forgoing arlicle in this proceeding(Gebreselassie & Kempferl, 2005) for a triaxial and one dimensionai compression loadingcondition. The influence of these parameters on the per-formance of an idealised excavation areinvestigated in this paper. By varying one parameter and keeping the other parameters constant,the influence of each parameter on the pedormance of the excavation can be studied.This study restrict itself to normaliy consolidated soft clays only, however, the result of the studymay also apply to other type of soils. The outcome of the sensitivity study may help the user tohave a clear picture of the influence of each parameter of a hardening soil model on thepedormance of an excavation. lt helps to judge the confidence interval of the variation of the soilparameters

2 The idealised excavation problem

ln order to perform the sensitivity study of the model parameiers, an ideaiised excavation shown in

Figure 1a has been chosen. The ground is assumed to be a deposit of a homogeneous lacustrinesoft soil with the ground water table located at 1.5 m below the ground surface. The excavation 6.0m deep is supporled by a sheet pile wall of the type Hoech 134 which has a total length of 12.0 mand an embedment depth of 6 m. The wall is suppofied by two level of struts of the type IPB 360 St37. A buiiding load o{ 50 kN/m2 ai a distance of 3 m behind the wall and a traific load of 10 kN/m2are assumed at the ground sudace.

327

.la)L,t l<__',, A__+? o*-g.o=0-q-l ro X

*;sr ;:- -- --- E: '1 "' Excav.

-l1l I-*----=-----r tiYli7.li^flO -3 txcav.

-4Q r=-

5 txcav.

GWI_______.1I

I

I

I

I

Lacustrine soft soil

- all dimensions are in m- dimensions are not to scale

-12.0-=]

F--36 No. of elements = 2009, No. of Nodes = 16499No. of stress points - 241A8

Figure 1. a) tdealized excavation, b) the finite element model and its mesh

3 The constitutive soil model

The constitutive model to which the soil parameters are being calibrated in this paper is an elasto-plastic-cap soil model known as the hardening soil model (HSM). The HSM is implemented in thefinite element code for soils and rocks "PLAXIS" (Brinkgreve,2002).lt is originally developed basedon the so called the Duncan-Chang hyperbo{ic model. lt, however, supersedes the hyperboiicmodel, because it uses the plasticity theory instead of the elasticity theory, it includes ihe dialatancysoil behaviour and it introduces the yield cap. The HSM also considers the stress dependantstiffness of the soil according to the power law. For detail lnformation on the constitutive model andthe program PLAXIS refer to Brinkgreve (2002) (see also Gebreselassie & Kempferl, 2005).As mentioned above, the HSM is used to simulate the soil behaviour, whereas a Mohr-CoulombModel (t\4CM) is used for the intefface elements. A drained type of analysis is chosen, because it isbelieved that this condition is most unfavourable condition for excavations in soft deposits. Thereference soil parameters required for the HSM are given in Table 1 and the soil parameteas for theinterJace elements according to the MCM are given in Table 2. The siiffness of the soil is adoptedas it is for the intedace element, whereas the shear strength parameter are reduced by a factor of1/3. The wall and the struts are assumed to behave linear elastic with the following materialpropediesat:

EA= 3.5g1 x 106 kN/m, El = 5.355 x 104 kN-m2/m, w.= 1.34 kN-m/ffi. v = 0.30Strut: EA = 3.801 x 106 kN, Lsp"cins = 2.0 m

Table 1. Reference soil parameters for the HSM

7"",

IkNim3] lkNim,l-)u

IkNim2]

-rcitr ^-.

IkNim2]

mRl

It t-l

K;"

ita

[']

-.2t-ur P

lkNlm2l [kN/rn2]

V,,

t-l

25.3 13.2 3253 z3+ö

)'a

0.63 0.83 0.573 A.201 9170 1 00

Table 2. Reference soil parameters for ihe iniedace elements according to the MCM

Tsat

IkN/m3]

a=1 a

LJ [kN/m,]

tr

lkNim2l

trtncreamenl J tei

[kNim2] [kNim2]

U.ret

ikNim2l

v

I-llq 5 AA etAe

4 The finite element model and the ealculation stages

An imporlant parl of the finite element model is shown in Figure 1b, The model is extended to adepth oI 42m where afixed boundary is imposed. At a distance of 36 m behindthe wall and atthesymmetry axis, a zero horizontal displacement is imposed. The size of the model as a whole is 48m wide and 42 m high. Triangular elements with '15 nodes are used in generating the mesh. Thiselement provides a fourlh order interpolation for displacements and it involves twelve numericalintegration stress points (Gauss points).The model consists of 2009 elements, 16499 nodes and24108 stress points.For the drained analysis of the idealised excavation problem, the HSM parameters in Table 1 areadopted as a reference parameiers for the soil body. ln order to study the sensitivity of the soilparameters, their values are varied above and below the reference values. The contact betweenthe wall and the soil body is simulated by mean of interJace elements whose material properties aregiven in Table 2.The following construction stages has been followed in the computation:

a^a

generation of the initial stresses (K6 - method)application of the surcharge and traffic loadsinstallation of the wallfirst excavationinstallation of the 1st strut and 2nd excavationinstallation of the 2nd strut and 3rd excavation

5 Analysis of ihe computation results

5.1 The effect of the variation of the Poisson's ralio vur

As it can be seen from Figure 2, the parameter yur seems to be a pure deformation parameter. ln otherwords, vur may affect the deformation of the wall and soil movements but not the eafth pressure andbending moment of the wall. A change in v* trom its reference value of 0.2 to a smaller

ä 130i() I

10

0

-1C

Stage 0:Stage 1:Stage 2:Stage 3:Stage 4:Stage 5;

7C -50 -30 -10 10-150 -50 50 -225 -150 -75 0 75 0 3 6 I 12

horizontal wall earlh pressure Bending moment distance from ihedeformation [mm] [kN/m1 [kN-m/m] symmetry axis

towards the wall [m]

Figure 2. The effect of the variation of y,. on a) deformation of the wall, b) earlh pressure, c)

bending moment of the wail, d) heave of the bottom of excavation, and e) settlement at the sudace

E

-c

oo

0rI

-1 L-öL

_f

Ä'-

cL"f-6 t-_l:/f-8r-o!"f

- lLi -I-11 --

,^|- tl -

trF 'cn:6 -soEc)

= -AAc)

CD

-50

-b( l

i2 18 24 3A 36 42 4l

disiance behindthe wall [m]

--€- Reference

---*- v,. = o.so

x0.)* 120oEI 110o

e 100

323

value of 0.05 and a larger t'alue of 0.3 has resulted in a uniform change of the wall deflection byabout -7 and 4% respectively. Simiiarly, a change of the heave by about i5 and -i}"k, and achange of the suijace settlement by about -21 and 15% respectively are calculared.

5.2 The effect of the variation of the coefficient of the eafth pressure at resi ,ri"

The HSM treats Ki' and K6separately. Whereas Ki" is a model parameter which is ciosely reiated

to the stiffness parameters Esl, Er,, Eoea a,od v*, Ko is purely used to define the initial state of thestresses. For normally consolidated soft soils, however, these values are more or iess the same.

The value of Ki" as a model parameter can not be varied indefinitely. For example, for the given

reference parameters, the minimum and maximum possible values of Ki" are 0.437 and 0.71

respectively. Here Ko is assumed to vary with Ki". As it can be seen from Figure 3, the parameter

Kj" would affect the deformation of the wall, the soil movements, the eafth pressure and bending

moment of the wall, although the magnitude of its influence is moderate as compare to the triaxialcase of loading (Gebreselassie & Kempferl, 2005). Varying the value of Ki" from the reference

value of 0.573 to those extreme values has resulted in a change of the maximum wall deformationof about -21 and 3% respectively. Similarly, a change of the heave by about 2 and -9"/", a changeof the sudace settlement by about -5 and 7"Ä, a change of the earth pressure by about -21 andB"k, and a change of the bending moment by about -18 and 2% respectively are calculated. From

the above percentage difference presentation and the Figure 3, it appears that varying lhe Ki"value towards the lowest limit is more sensitive than varying its value towards the upper iimit,although the difference between the reference vaiue and the extreme values is almost the same.

r l5U-E

7 tqoO

cg> rcn(n 'uuOx

Bending moment[kN-m/m]

0 3 6 9 12 121821 30364248disiance from ihe disiance behindsymmetry axis the wall [m]

iowards the wall [m]

Figure 3. The effect of the variation of Ki" on a) deformaiion of the wail, b) eafth pressure, c)

bending moment of the wall, d) heave of the bottom of excavation, and e) settlement at the surface

5.3 The effect of ihe variation of the failure factor R;

ln triaxial and oedometer loading condiiions, ii has been proved thai the failure factor Rl plays animporlant role in enhancing or retarding the failure of the soil body (Gebreselassie & Kempferl,2005). lts influence on ihe iciealised excavation, however. seems to be minimum, wiih excepiion ofthe settlement behind ihe wall (Figure a)). Varying the value of ,Qrfi'om ihe reference vaiue of 0.83

i\r'I

:

i ir, tI

:Ll :IiiIirl

Iö-_TEb :I

i iIiri,:.it:lji+

-50

1 press

lkN/ml

tt/t I I

fr+l tlD):M', II I l'

// 1ll'64tr l,'/i

- i I ,

/rtt!b: i I I i:,

l+ Reference i

l--e-K=0.4371-il---a-- Ko = 0.71 I tr+'J9

r 1 | i .&Tt lai+l' .#lrl i &trld)rrltT

,t il9:i 1 I i&l-f- I I f\t €j'-i0 -10 10-150

:al wall eafth50

re

i

i

'.4

rt

;

iI

;

U

E

toc)D

O -t- ---:-;--ffffi.i i2\i I , &1-rT \-/. : tlt -T

^l , &1 t'l : ///',1cL . ö4 I I

; i // /i.f : 'dd , T-al // /

- I 6 /'(---+:--5i // v II A ö l-_ä_-b - b, 4>'I ll i ;l-----a--zlfl f L-I f t' , {8it tr : -r

^t 4:Qi : i"i fl t , l -itoi S{ .,-iI &O: : it1]i \\ ij

12 [t] . I

-70 -50 -30 -10

horizontal walldeforrnation fmm

10

0

-tuEFon

-o -30EAJ

E -40o(f)

20

10

c)*toi-9 1

o-oc)1

c0

o9C(dc)

-60

-74

tc 0.67 and 0.97 has resulted in a change of the surface settlement by about -8 and 69," respec-tively. For all the other cases, the difference remains below +5%.

tr

.C

c)o

-r - (a)li',i

a' t- |:::

^i:li:j-ql) i

:t-si

- IUFtr ar.

c^-O -JUEo= _tA0)a

-an

-60

-74

l5u

14A

'130

120

110

100

EEc.o

(gOXq)

Eoo

_oG)

5(6

c)

o-a

horizontal walldeformation [mm]

eadh pressure

IkNim]

-50 -30 -10 10-150 -50 50 -225 -150 -75 0 75

Bending momentIkN-m/m1

036912distance from thesymmetry axis

towards the wall [m]

12 18 24 30 36 42 48

distance behindthe wall [m]

Figure 4. The effect of the variation of Eron a) deformation of the wall, b) earth pressure, c)bending moment of the wall, d) heave of the bottom of excavation, and e) settlement at the surface

5.4 The effect of the variation of the consirained modulus Eo"6

As shown in Figure 5, a variation of the constrained modulus Eo,a by about +50% its referencevalue, has resulted in a change of the maximum wall deflection by about -30 and 5% respectively.Similarly, a change of the heave by about -'17 and -4"/", a change of the sudace settlement byabout -24 and 2"/", a change of the maximum eafth pressure above the bottom of excavation byabout -17 and 2o/", and a change of the bending moment by about -23 and 3% respectively hasbeen observed (Figures 5). Hence, the following conclusion may be drawn with regard to theresponse of the excavation to the change of Eoea.

a) ln all cases Eoea is more sensible to a change of value below the reference value than tovalue greater than the reference. lt can be seen from Figure 6 that a reduction of thereference .;alue of Eoea by 50% has caused a reduction of the wall and soil movements,the active earth pressure and the bending moment by about 17 1o 307o, whereasincreasing the reference value by same amount (50%) show no significant influence (2 to5%), lt seems that the ratio of EsdEo"a is more impoftant than the absolute value of theEo"6.For the reference case, this ratio becomes 1.1. lf lhe Eo"a is increased or decreasedby about 50%, the ratio becomes 0.73 and 2.20 respectively. The ratio in the case ofincreasing Eo"a is more closer to the reference ratio than the other way round. This mightbe the reason why the change oI Eoea is more sensible to a value below ihe reference thanabove the reference value.

b) Contrary to expectation, a reduced value of Eo"6 has resulted in a reduction of wall and soilmovements.

c) Figure 6b shows a reduced active pressure and an increased passive pressure for thecase of Eoea smaller than the reference value. This again contradicts with the reduced wallmovement that is discussed in (b). A reduced wall movement would have resulted a higheractive pressure and lower passive pressure.

d) A reduced active pressure on one side and an increased passive pressure on the otherside has resulted in a reduced bending moment, which seems logical in respect to thegiven loading condition but not in a general sense.

ii--e- Reference:D-_n07

v ilI- v,J,

---*- Rr = 0.67

325

-a'- |-L ,

^l:

-4

-o

_1

-8

,9

10

11

12-100 -75 -50 -25 0 -150 -50 50

horizontal wall eafth pressuredeformation [mm] [kN/m]

Figure 5. The effect of the variationbending moment of the wall, d) heave

10m

-250 -150 -50 50 0 3 6 9 12 12 .,8 24 30 36 42 48

Bending moment cjistance from the distance behind[kN-m/m] symmetry axis the wall [m]

towards the wall [m]

at Ess6 on a) deformation of the wall, b) eanh pressure, c)of the bottom of excavation, and e) settlement at the surface

--€- Reference

^ n<vFrefv.! ^

Loed

-+- 1.s x EJd

'E -zvtr:_30

6 -qoFo -cnto(D -60

-7n

-80

- IJU-Ec 140o-=(d> r2nOX* 120oEI 110O-oa) 100

!

cd

o9oo

T1I

I

T

1II

T

"L

IITI

1

+II

_T1

5.5 The effect of the variation of the un/reloading modulus of elasticity Eu,

The reference value of Eur was directly taken from triaxial test result and it is equal to s.s.rjir(Gebreselasie,2003). Lowering the reference value Io z.tllr, which is usually recommended in

praciice with the absence of a test result, and further lowering the reference value to z.flij haveresulted in an increase of the displacement of the toe of the wall by about 27 and 637" respectively.Similarly, a change of the heave of the bottom of excavation by about 75 and 15A7", a change ofthe suface settlement by aboui -15 and 3Ok, a change of the active pressure above the bottom ofexcavation by about -16 and 22"/" respectively, and an insignificant change of the maximumbending moment (below 2.5 %) are calculated (Figure 6). The earth pressure below the excavationlevel on both active and passive side also shows no significant change relative to the referencevalue. Contrary to the expectation, the settlement at ihe surface for the reduced values of Eur is less

E

to_c)o

0

-l

-3

-4

-Ä

_A

-7

-8

-9

-10

-t I

E

S zeo

10

0

-i0

F-2nr*'tr5-30

E -ooE0)Fn

ötu) -60 i

-c 80-100-80 -60 -40 -20 0 -150 -50 5C -250 -'150 ,50 50 0 3 6 I 12 i2 18 24 30 36 42 48

horizontal wall earih pressure Bending moment distance from the distance behinddeformation [mm] ikNiml [kN-m/m] symmetry axis the vuall [m]

towards the wall lml

Figure 6. The effect of ihe variation of Euron a) deformaiion of the wall, b) earlh pressure, c)bending moment of the wall, d) heave of ihe boitom of excavation, and e) seitlement at ihe sudace

326

than iha'i fi'om the reference rvalue. This is mainly due io the upward displacement of ihe wall. Thewhole soil body seems to heave upwards due to lower values of Eu,

5.6 The effect of the variation of the secant modulus of elasticity Eso

Figure 7 shows the effect of the variation of Esc by t50% from its reference value. These varia-tions of Eso have resulted in a change of the maximum wall deflection by about 45 and -24"/"respectiveiy. Similar change of ihe heave by about 21 and 11"h, the sudace seirlement by about 71and -37"/o, the maximum earth pressure above the botiom of excavation by about'.l9 and -15%,and the maximum bending moment by about 27 and 1B% respectively has been observed.At first glance, it seems that an increased wall movement shouid result in higher passive resis-tance, because the soil is more close to the passive limit state. However, as the numerical study ofthe mobilisation of the passive resistance (Gebreselassie, 2003; Gebreselassie & Kempfed, 2005)also shows, the passive resistance is lower for lower values of the modulus for a given displace-ment of the wall and keeping the shear parameter constant. This is exactly what one can observein Figure 7. Lower value of Esa leads to higher wall movement but a lower passive resistance andvice versa.

'10

0

10----r---

---A- c--tri-30

F -+oEO.^Fc)u) -60

-70

-80

-901

50

40

30

20

10

'l

1

'1

1

1

1

EEc

=(ücdoxq)

oEoo-oc)-c.

cd

0)

cdo)

-C

-l-tl_I

I

TI

i

Ti

E

5o-oo

-uIi"7 1:s[-.

horizontal walldeformation [mm]

-iso -50 50 -2sa -150 -50 50

earth pressure Bending moment[kN/m] [kN-m/m]

036912distance {rom thesymmetry axis

towards the wall [m]

2182430364248distance behind

the wall [m]

Figure 7, The effect of the variation of Eso on a) deformation of the wall, b) eadh pressure, c)bending moment of the wall, d) heave of the bottom of excavation, and e) settlement at the sudace

6 Sunrmary

A sensitivity study of the soil parameters for HSM has been conducted based on an idealised ex-cavation in normally consolidated cohesive soils in order to study ihe influence of these parameterson the pedormance of an excavation. The result of the study may be summarised as follows:

E56 Seerns to lead the role of influencing the wall displacement, the earth pressure, thebending moment and the settlement behind the wall. Due to the non-linearity, however,increasing its value does not necessarily produce the same effect as the other way round .

Its influence on bottom heave is limited only to the heave near the wall and its influenceceases towards the middle of the excavation. E ,' plays a dominant role on the heave ofthe excavation and the displacement of the wall toe, but it has insignificant inf{uence onthe bending moment. vu, has oniy an etfect on the botiom heave and settlement at thesudace. Fr shows a negligible etfect on all the cases.Ki" value may affect the deformations, bending moment and the eafth pressure. although

aa1)/ /

the magnitude of its influence is moderate as compare to the triaxial state of stress. Kf"

value towards the lowest limit is more sensitive than varying its value towards the upperIimit, although the diiference between the reference value and the extreme values isalmost the same.

. The sensitivity study of the Eoea shows that the ralio EsdEo"a is more impoftant than theabsolute value of Eo"a.

7 List of Symbols and Abbreviations

Elit = .""unt modulus ai 50% of the failure & = ratio of the stress at failure and the

stress and at effeciive reference pressure of p'ef ultimate stress

Ef,'o=constrainedmodulus at p'4 K;" =coefficientof theearthpressureatEff' = unlreloading modulus

^t p'{ rest for normally consolidated soils

E = modulus of elasticity v u, = Poisson's ratio for un/reloading

7",, = saturated unit weight of soil v = Poisson's ratio

E = effective angle of intemal friction m = exponent in the power law

ö = wallfriction HSM = Hardening Soil Model

c' = effective cohesion MCM = Mohr-Coulomb Model

I ReferencesBrinkgreve R.B.J. 2002. Hand book of the finite element code for soil and rock analysis "PLAXIS". Balkema Publisher,

Rotterdam.

Gebreselassie B. 2003. Experimental, analytical and numerical investigations of excavations in normally consolidated soft soils.Dissertation, University of Kassel,.Schriftenreihe Geotechnik, Heft 1 4.

Gebreselassie B., Kempfert H.-G. 2005. Mobilisation of the eärth resistance of a normally consolidated cohesive soils. The Pro-ceedings of the 16tn lnternational conference on Soil Mechanics and Geotechnical Engineering, Osaka, Japan (in press).

Gebreselassie 8., Kempfert H.-G. 2005. Calibration of soil parameters for an elasto-plastic cap model under drained condiiion.The Proceedings of the 1 1s lnternational conference of IACMAG, Turin, ltaty (in this volume).

328

Proceedings of the Eleventh lnternational Conferenceon Computer Methods and Advances in Geomechanics

TORINO / ITALY I 19.24 JUNE 2OO5

Prediction, analysis and design lngeomechanical applications

Edited by:

Giovanni Barla and Marco BarlaDepartment of Structural and Geotechnical Engineering,

Politecnico di Torino, ltaly

VOLUME 1

PATRON EDITOREBOLOGNA 2OO5